Household transmission of the SARS-CoV-2 Omicron variant in Denmark

In late 2021, the Omicron SARS-CoV-2 variant overtook the previously dominant Delta variant, but the extent to which this transition was driven by immune evasion or a change in the inherent transmissibility is currently unclear. We estimate SARS-CoV-2 transmission within Danish households during December 2021. Among 26,675 households (8,568 with the Omicron VOC), we identified 14,140 secondary infections within a 1–7-day follow-up period. The secondary attack rate was 29% and 21% in households infected with Omicron and Delta, respectively. For Omicron, the odds of infection were 1.10 (95%-CI: 1.00-1.21) times higher for unvaccinated, 2.38 (95%-CI: 2.23-2.54) times higher for fully vaccinated and 3.20 (95%-CI: 2.67-3.83) times higher for booster-vaccinated contacts compared to Delta. We conclude that the transition from Delta to Omicron VOC was primarily driven by immune evasiveness and to a lesser extent an inherent increase in the basic transmissibility of the Omicron variant.


Background
This section provides some background information on the circumstances surrounding our study, i.e., the situation in Denmark between 1 st -31 st December 2021. Table S1 shows the number of cases identified with RT-PCR, the proportion of positive cases selected for Variant PCR testing and the proportion of positive cases selected for Variant PCR for which Omicron was detected.  (Table S2). All positive antigen tests were recommended by the authorities to be confirmed with an RT-PCR test. RT-PCR tests are more sensitive, 1 but also require a longer time before the result is known. The median time to known result is approximately 24 hours (Table S3). Only samples with positive RT-PCR test results were available for selection for Variant PCR and whole genome sequencing (WGS).  classifications were incorrect (Table S5). This extremely high agreement confirms that our study is not affected by any classification bias with respect to variant.

Causal assumptions
The causal effect of household exposure to the Omicron VOC rather than the Delta VOC on the SAR may be confounded. We assume that these differences are caused by the temporo-spatial patterns of transmission of the Omicron VOC when first introduced in Denmark (see appendix Figure S2).
The directed acyclic graph displayed in Figure S2 suggests a confounding pathway from variant to SAR via the initial chains of transmission through household characteristics. What the graph encodes is that we believe that any differences between households exposed to the Omicron VOC and those exposed to the Delta VOC are due to the particularities of how Omicron was initially spread throughout the community. While the Delta VOC was widespread at the start of the study period, the Omicron VOC was not widespread. The household structure and other characteristics of the households exposed to the two variants might therefore differ. A causal interpretation of our findings is conditional on the assumption that all effects of the non-random assignment of variants to households are intercepted by conditioning on the observed household characteristics. We note that this will also diminish any household unobserved characteristics that are associated with the observed characteristics, e.g., age-related behavioral factors will be indirectly adjusted through the adjustment for age. 3 Descriptive statistics In this section, we provide additional descriptive statistics on our study sample.
Appendix Table S6 shows the summary statistics at the level of primary case (this augments Table   1, which shows the summary statistics for primary cases and contacts separately).
Appendix Tables S7 and S8 show more detailed summary statistics on the vaccination status of individuals within the "Fully vaccinated" category.
Appendix Table S9 shows the SAR and number of observations by vaccination status of both the primary case and contact.
Appendix Table S10 shows SAR and number of observations by vaccination status and age of the primary case.
Appendix Table S11 shows SAR and number of observations by vaccination status and age of the contact.
Appendix Table S12 shows SAR and number of observations by household size and vaccination status of the contact.  Notes: Summary statistics are not aggregated on the primary case level. Unvaccinated includes 7 primary cases with partial vaccination and 52 contacts with partial vaccination.     4.1 Viral load of primary cases Figure S3 shows the density of sample Ct values of primary cases stratified by the Omicron VOC and Delta VOC.

Misclassification of cases
One of the main potential weaknesses of our approach is the assumption that primary and secondary cases are classified correctly, i.e., that the presumed within-household transmission did in fact occur from primary to secondary household cases. There are three overall concerns with misclassifications: i) Tertiary cases could be misclassified as secondary cases; ii) Misclassification of primary cases iii) Secondary cases are identified as being infected in the household, but are in fact infected by the outside community. We address these three overall concerns below. Lastly, we investigate the impact on our results from the potential pollution from misclassification of cases.

i) Misclassification of tertiary cases as secondary cases
Tertiary cases could in theory be misclassified as secondary cases. This should not pose an issue when comparing variants, as long as the misclassification is the same across variants. However, if one variant has a shorter serial interval time, as the Omicron VOC has been suggested to have 2 , this could lead to a difference in the misclassification that is correlated with the household variant. To address this, we use two-person households as a validation measure, because they do not include tertiary cases. Figure S4, panels a-b shows the testing propensity for the overall sample (  Notes: Panels a and c shows the same as Figure 1, whereas panels b and d are stratified by 2-person households. Panels a-b show the probability of potential secondary cases being tested after a primary case has been identified within the household. Panel c-d show the probability of potential secondary cases that test positive subsequently to a primary case being identified within the household. Note that the latter is not conditional on being tested, i.e., the denominator contains test negative individuals and untested individuals. The x axes show the days since the primary case tested positive, and the y axes show the proportion of individuals either being tested (a) or testing positive (b) with an RT-PCR test, based on the variant of the primary case. The SAR for each day relative to the primary case can be read directly from panels c-d. For example, in panel c the SAR on day 7 is 29% for Omicron (red) and 21% for Delta (blue), whereas the SAR on day 4 is 22% for Omicron and 15% for Delta. The markers show the point estimates of the mean. The shaded areas show the 95% confidence bands clustered on the household level.
Next, using the SAR estimates from panel b, we can calculate the relative SAR in Omicron households compared to Delta households. If the increased serial interval for Omicron implied more tertiary cases, we should see an increased difference in the relative SAR over time for households with more than two members. We find no indication of a difference in the relative SAR of households infected with the Omicron VOC relative to those infected with the Delta VOC across household size (Table  S13). This suggests that differences in the probability of misclassification of tertiary cases as secondary cases across variants is negligible, and thus not a major limitation in our study.
Lastly, we note that the levels of the SAR in two-person households differ from the SAR in larger households, which might be due to unobserved differences in characteristics related to transmission. However, we have no reason to believe any differences across variants within household size, i.e., that the two-person households infected with the Omicron VOC are inherently different from those infected with the Delta VOC.  Figure S4 panels c-d.

ii) Misclassification of primary cases
Correct identification of primary cases within the household is important for this study as this determines whether the household is counted as an Omicron or Delta household when assessing the effect of the VOC on transmission. In theory the first identified case, i.e., the index case, may not be the primary case of a household transmission chain. Correct identification of primary cases is important for our estimates of infectiousness from primary cases, as infectiousness is correlated with age, vaccination status, and viral load. In our setting, we use the timing of tests and test results to classify cases. This could be an issue, if for example vaccination status and/or symptoms are correlated with the likelihood of being tested. The optimal setting would be to test all household members on, say, a daily basis to make sure of the temporal ordering between the primary and secondary cases. We do not have that, but Denmark had a high test capacity and test intensity, which leaves us with a large proportion of contacts actually having several test results within 7 days of exposure.
Overall, we can classify the relevant household contacts into five types by their observed tests and test results from two tests within 7 days of exposure: Using this sub-sample, we estimate our full regression model again. The estimates are relatively robust to this sub-sampling (Table S21, model XI).
Finally, to reduce the probability of misclassifying primary cases as secondary cases, we only include secondary cases found on day 2-7 and 3-7. This accounts for the possibility that an individual that was previously infected may self-present for a test the day after another person in the same household that they themselves infected. The results (Table S19, column V and VI) are qualitatively similar to the main results presented in the paper, which further supports the overall robustness of our conclusions. iii)

Misclassification of community cases as secondary household cases
Lastly, secondary cases could in theory be infected by the outside community and not the household and therefore be misclassified as secondary household cases. To address this potential concern of misclassification, we first investigate the probability that secondary cases are infected with the same variant as the primary case. In households where the primary case was infected with the Omicron VOC, we found 4,090 secondary cases that also had a Variant PCR result (Table S15). Of these, 4,010 (98%) were also Omicron VOC and 80 (2%) were Delta VOC. Similarly, in households where the primary case was infected with the Delta VOC, we found 7,420 secondary cases. Of these, 7,209 (97%) were also Delta and 211 (3%) were Omicron VOC. The overall intra-household correlation of variants was 97.5 (CI: 97.1-97.8). We interpret this as the possibility of misclassification being negligible. This measure is, however, a necessary-but not sufficient-condition. If the local geographic neighborhood is primarily infected with one variant and that is the same as within the household, we would not be able to separate secondary cases infected in the household from those infected in the local community based on the variant. However, for households infected with a different variant from that which is dominant in the neighborhood, we can in fact gauge the role of misclassified community infections. To this end, we calculated the overall incidence ( Figure S5, a) and the share of Omicron cases ( Figure S5, b) for each of the 98 municipalities in Denmark. Thus, we can follow households infected with Omicron that are surrounded by a neighborhood with Delta. Here, we would expect the secondary cases to be infected with Omicron, if they were infected in the household, and infected with Delta, if they were infected in the community. And vice versa for Delta households situated in Omicron neighborhoods. We categorized municipalities into four quartiles based on their proportion of Omicron cases. We then again estimated the probability that the secondary case has the same variant as the primary case. We found a strong correlation for households infected with the Omicron VOC-across all municipality incidence quartiles. For households infected with the Delta VOC, we find a 5 percentage point (on a baseline of 99%) lower probability in municipalities with the highest proportion of Omicron cases (Table S16, specification I). Moreover, we found little evidence that the estimates of misclassification were driven by households located in municipalities with either low or high overall case incidence (specification II and III). Indeed, this suggests that there is some are some contamination of household secondary cases for Delta households, but also that the misclassification is limited. The incidence quartiles are number of cases per 1,000 inhabitants: Q1=13, Q2=16, and Q3=26. The geospatial patterns of the incidence and omicron case proportions are illustrated in Figure S5.

Impact of misclassification on our estimates
If a substantial number of secondary cases were more or less randomly infected with the Delta vs the Omicron VOC from outside the household, then we expect that the within-household correlation would be lower than we observed. However, it could also be argued that a high correlation may result from a sufficiently strong local-level spatial component in the spread of variants. In this case, a natural geographical correlation in the variant with which a case is infected would be expected to affect both the primary and secondary case within the household, as the geographical location of the household is fixed. Therefore, the intra-household correlation of variants would be biased upwards compared to the real effect of secondary cases being infected by the primary case, as secondary cases are overcounted. However, the misclassification would only affect the OR estimates reported in the paper if the misclassification is not proportional to the stratum-specific odds of testing positive. If one assumes that the misclassification is proportional to the risk such that the percentage that is misclassified is the same in low-and high-risk strata. Such a proportional mechanism would work to inflate the estimates, but to a limited extent. The misclassification would also shrink the confidence intervals, but not substantially under reasonable assumptions. Appendix Table S17 shows how our effect sizes would be influenced under different levels of misclassification. We believe that the effects are unlikely to materially change the conclusions of the analyses, even under more severe assumptions that those assumed here. Table   S17 shows the OR estimates with no misclassification of cases (column 1), 10% misclassification (column 2), and 30% misclassification (column 3). 4.3 Time since vaccination for positive secondary cases Figure S6 shows the distribution of days since last vaccination/infection for secondary cases, stratified by the household VOC and time since vaccination of both the primary and secondary case.
The panels show there is no obvious trend in the waning immunity across variants. Note the groups of booster-vaccinated primary and secondary cases are from a low number of cases, which limits precision.

Robustness of main results
This subsection provides results of additional analyses using different model specifications in order to validate the results shown in the main paper.
The test probabilities for RT-PCR test alone are shown in Figure S7 (this augments Figure 1, which also includes antigen tests). Similarly, Figure S8 shows the same as Figure 1, but using a 14-day follow-up period in place of the 7-day period shown in the main paper. The patterns are qualitatively similar to these different potential assumptions. Notes: This figure shows the same as Figure 1, but only including RT-PCR tests. Panel (a) shows the probability of potential secondary cases being tested after a primary case has been identified within the household. Panel (b) shows the probability of potential secondary cases that test positive subsequently to a primary case being identified within the household. Note that the latter is not conditional on being tested, i.e., the denominator contains test negative individuals and untested individuals. The x axes show the days since the primary case tested positive, and the y axes show the proportion of individuals either being tested (panel a) or testing positive (panel b) with an RT-PCR test, based on the variant of the primary case. The SAR for each day relative to the primary case can be read directly from panel (b). For example, the SAR on day 7 is 28% for Omicron (red) and 20% for Delta (blue), whereas the SAR on day 4 is 21% for Omicron and 14% for Delta. The markers show the point estimates of the mean. The shaded areas show the 95% confidence bands clustered on the household level. Notes: This figure shows the same as Figure 1, but with a 14-day follow-up period. Panel (a) shows the probability of potential secondary cases being tested after a primary case has been identified within the household. Panel (b) shows the probability of potential secondary cases that test positive subsequently to a primary case being identified within the household. Note that the latter is not conditional on being tested, i.e., the denominator contains test negative individuals and untested individuals. The x axes show the days since the primary case tested positive, and the y axes show the proportion of individuals either being tested (a) or testing positive (b) with an RT-PCR test, based on the variant of the primary case. The SAR for each day relative to the primary case can be read directly from panel (b). For example, the SAR on day 7 is 29% for Omicron (red) and 21% for Delta (blue), whereas the SAR on day 4 is 22% for Omicron and 15% for Delta. The markers show the point estimates of the mean. The shaded areas show the 95% confidence bands clustered on the household level.
To investigate the robustness of our main results, including the underlying assumptions, we re-ran the models to specific strata of the data. The estimates obtained from the same logistic regression model fit to each data subset are shown in Tables S18-S22, where Columns I-XII refer to the   following: I) The analysis presented in the main manuscript (for reference).
II) Using 14 days of follow-up, rather than 7 days. III) Restricting the household contacts to those having obtained a test, rather than all members of the same household.
IV) Excluding all households with a previous infection.
V) Only including secondary cases identified on day 2-7, rather than days 1-7.
VI) Only including secondary cases identified on day 3-7, rather than days 1-7.
VII) Excluding all households with a primary case younger than 10 years.
IX) Excluding all individuals with partial vaccination.
X) Controlling for Ct value of the primary case using an additional explanatory variable.
XI) Only including households where all contacts have been tested negative subsequent to the primary case.
XII) Splitting the "Fully vaccinated" category into four categories for both the primary case and household contact.
The results are qualitatively similar between these 11 different analyses, which further supports the robustness of our conclusions.
In Table S23, we further provide unadjusted estimates for the infectiousness and susceptibility, i.e., excluding the control variables age, sex, and household size.